On the Trans-Siberian Railway, it takes six days to chug from Moscow all the way to Beijing. That's if you decide to do the whole journey in one go.

Some people choose to do this: Those who want the undiluted train experience, or are going on business, or have small children in tow. One couple, traveling with their four young kids, told me just the thought of unloading and reloading their bags more than once gave them heart palpitations. I get that.

But if you have the time, definitely opt for at least one layover. That breaks up the monotony and allows for a couple of real baths (Only first-class passengers have showers in their train compartments. Everyone else makes do with wipes or whatever ablutions can be performed at a sink on a swaying train. We all pretend to lose our sense of smell).

I stopped twice -- the first in Siberia in the city of Irkutsk, and the second in Ulan Bator, Mongolia. I was especially excited about Mongolia -- it doesn't rank high on many must-visit lists, but its national parks are reputed to be stunningly beautiful.

On a Tuesday in October, I disembarked at the Ulan Bator train station. Bobby, the owner of the guesthouse I stayed in, picked me up and gave me a brief tour of the city.

Ulan Bator is chock full of Soviet-era style buildings, interspersed occasionally with a modern high-rise or Buddhist temple. Nearly half of Mongolia's three million people have squeezed into the capital city. A lot of young people are choosing to leave the nomadic life behind, Bobby said, in search of modernity and fortune (That's led to a growing homeless and housing crisis).

There are plenty of sights and restaurants there to visit. My absolute favorite was the International Intellectual Museum (no photos allowed inside, unfortunately).

It's a privately-owned museum dedicated to showcasing Mongolia's deep history of games and puzzles. Thousands of toys, puzzles and playthings are on display, either made or collected by its founder, toy maker Zandraa Tumen Ulzii. A tour guide leads visitors through floors full of traditional Mongolian games using ankle bones or interlocking wooden pieces, and encourages people to try their hand at solving a few simple ones. The museum also has dozens of elaborate chess sets carved out of wood, bone and stone (most made by Ulzii). The most intricate puzzle requires over 56,000 moves.

The museum is a sheer delight -- go, spend a few hours, you won't regret it.

But first, Genghis Khan

But my main purpose in stopping in Mongolia was to get out of the city and sleep in a ger, or the traditional Mongolian felt yurt.

Through my guesthouse, I signed up for a two-day stay at Gorkhi-Terelj National Park, which is about 35 miles northeast of Ulan Bator. The trip, including a driver, food and an overnight stay, came out to $60 (the entrance fee into the park is 3,000 Mongolian tugriks, or roughly $1.25). I was paired with two other guests, Matt and Pete; together, we set off early in the morning.

First, we made a pit-stop at an enormous statue of Genghis Khan riding on horseback.

Erected in 2008, the statue stands 130 feet tall and is reportedly made from 250 tons of stainless steel. You can dine at the restaurant inside and ride the elevator up to the horse's head to take in the view. The main complex is surrounded by gers and more statues.

The statue is an interesting sight to behold, but not incredibly historic or spell-binding in any way. If you are crunched for time, I'd recommend skipping this.

Gers inside the park

When we finally made it to Gorkhi-Terelj National Park, I spent a few hours simply admiring the magnificent view. The season was tipping into autumn, and the mountain ranges were already covered with golden trees, like blonde whiskers on chins. Cattle meandered about, and a couple of muscular camels trotted by later that day. Clusters of gers dotted the sides of the dirt road that wound through the park.

I was in heaven. The scenery was so gorgeous, the air smelled so clean (Ulan Bator is extremely polluted) and the whole ger/sleeping situation was so thrillingly new.

And let's not forget the horses.

Later that afternoon, the three of us rode horses, guided by an older gentleman, who said he originally hailed from Russia. None of us were terribly confident at riding, so it took a good hour before our horses would listen to us. We rode through fields of trees and over hills, and occasionally hung on for dear life when the horses decided to canter and gallop instead of amble along.

Three hours in, we stretched our legs by hiking up to the Aryabal Meditation Temple located inside the park. Getting there required crossing a bridge and climbing many steps. The inside of the temple was beautiful. The view was spectacular.

By dusk, the temperature had plunged, and our host came by to light the wood-fired stove. We dined on some veggies and beef (which I suspect was freshly slaughtered that day), and then hit the sack.

The gers are giant puzzles. The underlying wooden frame is made up of pieces that slide in together, with a felt cover on top. The exposed ceiling latticework inside was painted a bright orange. Each ger is quite roomy; ours held four twin beds, along with a table, a loveseat and the stove.

We rotated fire-stoking duties throughout the night, which is VERY important. If the fire dies, the gers only offer lukewarm protection against the cold mountain night.

The next day we lounged around and befriended our host family's extremely affectionate and shaggy cat. After several rounds of belly rubs, we packed up and headed back to Ulan Bator in the early afternoon. On the way back, we all agreed that coming back and seeing more of Mongolia had become a priority.